Period and index of genus one curves over global fields |
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Authors: | Shahed Sharif |
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Institution: | 1. California State University San Marcos, San Marcos, CA, 92096, USA
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Abstract: | The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over a given global field, as long as the characteristic of the field does not divide the period. |
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